I read it, but can't believe it. That would mean a dice that rolls heads 3.25% times more often than it rolls tails would only lose 0.02% of the entropy after 256 rolls.
Yes.
I would expect this 2-to-1-dice to create much less entropy. Please convince me you used the correct formula.
You are correct. I used Shannon's formula. There are many good answers about the "why" part in here:
https://math.stackexchange.com/questions/331103/intuitive-explanation-of-entropy